(2) Then we derive the partially observed global maximum principle. Compared to [1]} and [2]}, our result is both a correction and an extension. To our best knowledge, in the optimal control problems, we initiate to consider that the observation equation is not only driven by the Brownian motion, but also by the Poisson random measure. Moreover, the correlated noises between state and the observation equation not only come from the Brownian motion, but from the Poisson random measure. It is an extension of the case in [3]}, in which an LQ problem with special Poisson process and convex control domain is considered.
